How do you find an equation that describes the sequence #16, 17, 18, 19,...# and find the 23rd term?

2 Answers
Jun 30, 2017

Answer:

#a_n = n + 15#
#a_23 = 38#

Explanation:

To find an equation, we should use the arithmetic sequence formula:

#a_n = a_1 + (n-1)d#

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When using this formula, you need to find the values for #d# and #a_1#.

1. Finding #d# (common difference)

We are given the sequence #16, 17, 18, 19, ...#. Using this information, we can find the common difference (#d#), which is another way of saying the difference between any two consecutive numbers in the arithmetic sequence. You could find #d# in a number of ways:

#17 - 16 = 1#
#18 - 17 = 1#

etc.

But whatever way you choose to find it, you should get that #d = 1#.

2. Finding #a_1#

#a_1# is the first term of the sequence. In our case, #a_1# = 16.

3. Plug into the formula.

#a_n = 16 + (n-1)(1)#

Now distribute #1# to #(n-1)#:

#a_n = 16 + n - 1#
#a_n = n + 15#

That's your equation!

Now plug in 23 for #n#:

#a_23 = 23 + 15#
#a_23 = 38#

Jun 30, 2017

Answer:

#a_n=n+15" and " a_(23)=38#

Explanation:

#" this is an arithmetic sequence"#

#"the nth term is " a_n=a+(n-1)d#

#"where " a " is the first term and " d" the common difference"#

#"here " a=16" and " d=1#

#rArra_n=16+n-1=n+15#

#rArra_(23)=23+15=38#